Chapter 2: FAQs 89
variance because fewer data points are used in its cal-
culation.
Treynor Ratio The Treynor orReward-to-variability Ratio
is another Sharpe-like measure, but now the denomin-
ator is the systematic risk, measured by the portfolio’s
beta, (seeCapital Asset Pricing Model), instead of the
total risk:
Treynor ratio=
μ−r
β
.
In a well-diversified portfolio Sharpe and Treynor are
similar, but Treynor is more relevant for less diversified
portfolios or individual stocks.
Information Ratio The Information ratio is a different
type of performance measure in that it uses the idea
of tracking error. The numerator is the return in excess
of a benchmark again, but the denominator is the stan-
dard deviation of the differences between the portfolio
returns and the benchmark returns, thetracking error.
Information ratio=
μ−r
Tracking error
.
This ratio gives a measure of the value added by a
manager relative to their benchmark.
References and Further Reading
Modigliani, F & Modigliani, L 1997 Risk-adjusted performance.
J. Portfolio Manag. 23 (2) 45–54
Sharpe, WF 1966 Mutual Fund Performance.Journal of Business
January 119–138
Sortino FA & van der Meer, R 1991 Downside risk.J. Portfolio
Manag.27–31
Treynor, JL 1966 How to rate management investment funds.
Harvard Business Review 43 63–75
